Approximation of the Range Ambiguity Function in Near-field Sensing Systems

This paper investigates the range ambiguity function of near-field systems where bandwidth and near-field beamfocusing jointly determine the resolution. First, the general matched filter ambiguity function is derived and the near-field array factors of different antenna array geometries are introduced. Next, the near-field ambiguity function is approximated as a product of the range-dependent near-field array factor and the ambiguity function due to the utilized bandwidth and waveform. An approximation criterion based on the aperture-bandwidth product is formulated, and its accuracy is examined. Finally, the improvements to the ambiguity function offered by the near-field beamfocusing, as compared to the far-field case, are presented. The performance gains are evaluated in terms of resolution improvement offered by beamfocusing, peak-to-sidelobe and integrated-sidelobe level improvement. The gains offered by the near-field regime are shown to be range-dependent and substantial only in close proximity to the array.